On the solvability of the generalized Neumann problem for a higher-order elliptic equation in an infinite domain

We consider the generalized Neumann problem for a $2l$th-order elliptic equation with constant real higher-order coefficients in an infinite domain containing the exterior of some circle and bounded by a sufficiently smooth contour. It consists in specifying of the $(k_j-1)$th-order normal derivatives where $1 \le k_1 <\ldots <k_l \le 2l;$ for $k_j = j$ it turns into the Dirichlet problem, and for $k_j = j + 1$ into the Neumann problem. Under certain assumptions about the coefficients of the equation at infinity, a necessary and sufficient condition for the Fredholm property of this problem is obtained and a formula for its index in Hölder spaces is given.